On the Basic Representation Theorem for Convex Domination of Measures

J. Elton, Georgia Institute of Technology - Main Campus
Theodore P. Hill, Georgia Institute of Technology - Main Campus

Article comments

Copyright © 1998 Elsevier. The definitive version is available at http://dx.doi.org/10.1006/jmaa.1998.6158.

NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.

Abstract

A direct, constructive proof is given for the basic representation theorem for convex domination of measures. The proof is given in the finitistic case (purely atomic measures with a finite number of atoms), and a simple argument is then given to extend this result to the general case, including both probability measures and finite Borel measures on infinite-dimensional spaces. The infinite-dimensional case follows quickly from the finite-dimensional case with the use of the approximation property.